Title:  Symplectic duality via geometric Satake equivalence

Abstract:  Let X be a symplectic complex algebraic variety with a Hamiltonian action of a complex reductive group G. 
The classical construction of hamiltonian reduction X///G (Higgs branch) produces a Poisson variety (symplectic if smooth). 

In this century, there appeared more advanced constructions (starting from X,G) of Poisson varieties (some equipped with hamiltonian actions) with origins in physics and with applications to the relative Langlands program (Coulomb branch, S-duality). They use the geometry of the affine Grassmannian Gr_G, and notably the geometric Satake equivalence.  

We will study these constructions starting with a review of the geometric Satake equivalence.

Prerequisites: reductive groups, equivariant cohomology, derived categories of sheaves.Coulomb branches

Tentative plan: 1. Affine Grassmannians.
2. Geometric Satake equivalence.

3. Derived geometric Satake.

4. Coulomb branches of cotangent type.

5. Coulomb branches of noncotangent type.

6. Examples: toric hyperk\"ahler varieties and quiver gauge theories.